# Introduction To Graphs Questions

We provide introduction to graphs practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on introduction to graphs skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom.

#### List of introduction to graphs Questions

Question No Questions Class
1 Rectangle bars touching each other in which graph
A. histogram
B. bar
c. pie
D. line
8
2 Find the value of ( p ) if the points
( (2,1),(p,-1) ) and (-1,3) are collinear.
8
3 Write the ratio of the heights of
highest peak and the lowest peak.
A .22: 15
B . 15: 22
( c, 20: 13 )
D. 13: 22
8
4 The bar chart shows the number of
workers employed by a trading companyin three years. Calculate the
difference between the total number of
male and female workers employed over
those three years.
( mathbf{A} )
B. 2
( c cdot 4 )
D.
8
5 Find the ratio of the total sales of laptop
in Rajasthan state for both years to the
total sales of laptop in Gujarat state for both years?
Sales of laptop
( A cdot 8: 13 )
B. 13: 8
c. 11: 8
D. 8: 11
8
6 With the help of which of the following
will you describe the position of a pen
on a table?
A. Coordinate geometry
c. Trignometry
D. Proportions
8
7 Find the bar graph and state why? 8
8 Using graph paper, (take ( 2 mathrm{cm}=1 ) unit on both axis), plot ( boldsymbol{A}(-mathbf{4}, mathbf{2}) ) and ( boldsymbol{B}(mathbf{2}, mathbf{4}) )
( A^{prime} ) is the image of ( A ) when reflected in
the ( y ) -axis. Plot it on the graph paper
and write the coordinates of ( A^{prime} . B^{prime} ) is
the image of ( B ) when reflected about the
line ( A A^{prime} . ) Join ( A-B-A^{prime}-B^{prime} ) and
name the quadrilateral
8
9 Points (-3,-3),(4,-1),(6,6) and (-1,4)
when joined in the given order form a
A. parallelogram
B. rectangle
c. rhombus
D. square
8
10 The graph above shows the number of
units sold in 2015 for five different
video games console. The price of
consoles ( A, B, C, D, ) and ( E ) are ( \$ 100, ) ( \$ 150, \$ 200, \$ 250, ) and ( \$ 300 )
respectively. Which of the five consoles generated the most total revenue?
A . ( A )
в. ( B )
( c . D )
( D )
8
11 Consider the following data gathered from a survey of a colony:

Cricket ( begin{array}{ll}text { Favourate } & text { cricket } quad text { Basket } \ text { port: }end{array} ) sport:
1240 470 watching
Participating 620 320
Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph? Which sport is most popular?

8
12 Choose the correct answer from the
alternatives given :
Directions for questions 71 to 75: Study the following graph carefully to answer these questions.

Production (in lakh tonnes) of six units
of a company in 2006 and 2007 What is the difference in the production (in lakh tonnes) of all companies in
( mathbf{2 0 0 6} ) and ( mathbf{2 0 0 7} ) ?
ロ2006 므200
A . 45
В. 75
( c cdot 100 )
0.125

8
13 The performance of students in 1 st term
and 2 nd term is as given below. Draw a double bar graph choosing appropriate scale and answer the following:
Hindi Maths Subject: English
( 1^{s t} t e r m: ) 1 67 72
( 2^{n d} ) term:
70 65
In which subject, has the children improved their performance the most?
8
14 The mid-points of the side of a triangle ( operatorname{are} D(6,1), E(3,5) ) and ( F(-1,-2) ) then
the vertex opposite to D is
A. (-4,2)
в. (-4,5)
c. (2,5)
(年. (2,5)
D. (10,8)
8
15 In which graph, frequency is represented by the area of each rectangle?
A. bar
B. pie
c. line
D. histogram
8
16 If ( A ) and ( B ) are two points having coordinates (3,4) and (5,-2)
respectively and ( P ) is a point such that ( P A=P B ) and area of ( P A B=10 ) sq. units, then coordinates of ( mathrm{P} ) are
в. (7,2)( &(1,0) )
c. (2,7)( &(4,13) )
D. (7,4)( &(13,4) )
8
17 If the line ( 3 x-4 y=lambda ) cuts the circle
( x^{2}+y^{2}-4 x-8 y-5=0 ) in two
points then limits of ( lambda ) are
A . [-35,15]
В . (-35,15)
c. (-35,10)
D. (-35,15]
8
18 The following table shows the interest paid by a company (in lakhs):
( begin{array}{lll}text { 1995- } & text { 1996- } & text { 1997- }end{array} ) Year
Interest
in lakhs
[
20
]
25
of rupees)
Draw the bar graph to represent the above information.
8
19 Find the coordinates of the point on the
X-axis which is at distant 5 units from
( A(4,4) )
8
20 Co-ordinate of point P on a number line is
7. Find the coordinate of point on the
Number line which is at a distance of 8
units right to point ( P )
8
21 Choose the correct answer from the
alternatives given :
Directions for questions 71 to 75: Study
the following graph carefully to answer
these questions. Production (in lakh tonnes) of six units
of a company in 2006 and 2007

What is the average production of all
units (in lakh tonnes) for the year ( 2007 ? )
ロ 2006
A . 95
B. 92
( c .87 )
D. 93

8
22 A graph showing two sets of data simultaneously is known as
A. pictograph
B. histogram
c. pie chart
D. double bar graph
8
23 Let ( (x+y, 1) ) and ( (3, x-y) ) be equal
ordered pairs then find the value of ( x, y )
8
24 Answer the Following:
Explain the techniques of drawing a Histogram.
8
25 Total sales of branches ( B_{1}, B_{3}, ) and ( B_{5} )
together for both the years (in
thousand numbers) is:
( A cdot 250 )
3. 310
( c .435 )
0.560
8
26 The equation of line perpendicular to ( boldsymbol{x}=boldsymbol{c} ) is
( mathbf{A} cdot y=d )
B. ( x=d )
c. ( x=0 )
D. None of these
8
27 Give Reasons
A histogram is not a diagram.
8
28 Total sales of branch ( B_{6} ) for both the
years is what percent of the total
sales of branch ( B_{3} ) for both the years?
A. ( 68.54 % )
в. ( 71.11 % )
( c .73 .17 % )
D. ( 75.55 % )
8
29 Which city has more people reading newspaper than watching T.V?
When reading newspaper people watching TV
A. Patna
B. Kolkata
C. Mumbai
D. Delhi
8
30 The point ( left(x_{1}, y_{1}right),left(x_{2}, y_{2}right),left(x_{1}, y_{2}right) ) and
( left(x_{2}, y_{1}right) ) are always ( ? )
A. Collinear
B. concyclic
c. vertices of square
D. vertices of a rhombus
8
31 Name the axis on which following point
lie
(-5,-8)
8
32 Draw a triangle whose side are
represented by ( boldsymbol{x}=mathbf{0}, boldsymbol{y}=mathbf{0} ) and ( boldsymbol{x}+ )
( boldsymbol{y}=mathbf{3} ) in the Cartesian system Also find
the coordinates of its vertices.
8
33 Give Reasons
A frequency polygon can be drawn with the help of a Histogram.
8
34 What is the average sale of all the
branches (in thousand numbers) for the
year ( 2006 ? )
( A cdot 73 )
( B .80 )
( c cdot 83 )
0.88
8
35 Fill in the blanks with suitable word:
The ( x ) -coordinate is called as
8
36 What is the ratio of the total sales
of branch ( B_{2} ) for both years to the
total sales of branch ( B_{4} ) for both years?
( A .2: 3 )
( B .3: 5 )
( mathbf{C} cdot 4: 5 )
D. 7: 9
8
37 In which city number of people
watching T.V is same as people reading
newspaper?
( mathbb{Z} ) people reading newspaper
( A ). Delhi
B. Mumbai
C. Kolkata
D. Patna
8
38 In a statistical diagrammatic representation, rectangular bars drawn after a discontinuous series is called
graph.
A. bar
B. histogram
c. pie
D. frequency curve
8
39 Consider a square of side length 1 unit.
What is its area?
8
40 The following pie chat gives the marks second in an examination by a student
in Hindi, English, Mathematics, Social
Science and Science. If the total marks
obtained by the student were 540 answer the following questions. All values are shown in degrees.
Examine whether the sum of the marks
obtained in Social Science and
Mathematics is more than that in
Science and Hindi.
8
41 During the period ( 2007-2010 ), the
minimum rate of increase in sales is in
the case of?
A. Dove
3. Himalayas
c. Detto
D. Lux
8
42 Which is a two dimensional graph?
( A cdot ) pie
B. bar
c. histogram
D. frequency curve
8
43 The diagram is drawn on a square grid
Of the triangles marked ( P, Q, R ) and ( S )
which is the image of triangle ( X ) under
a reflection in the line ( M N ? )
( A )
3. ( Q )
( c . R )
( D )
8
44 Write the length of the perpendicular drawn from the point ( P(3,5,12) ) on ( x )
axis.
8
45 In a triangle ( A B C, ) the co-ordinates of
vertices ( A, B ) and ( C ) are (4,7),(-2,3)
and (0,1) respectively. find the
equation of median through vertex ( boldsymbol{A} ) Also, find the equation of the line
through vertex ( B ) and parallel to ( A C )
8
46 Study the graph carefully and answer
the question:
The number of people who prefer
playing Tennis in 2006 is how many millions less than the number of people
who prefer playing Tennis in ( 2005 ? )
A . 110
B . 105
( c .100 )
D. 95
8
47 When proving that a triangle is a right triangle using coordinate geometry
methods you must
A. show that the slopes of two of the sides are negative reciprocals creating perpendicular lines and right angles
B. show that the lengths of the sides satisfy the Pythagorean Theorem thus creating a right angle
C. both choices 1 and 2 may be used
D. neither choice 1 nor 2 may be used
E. none of these
8
48 Given below are some points, with thei
( boldsymbol{P}(mathbf{4}, mathbf{3}), boldsymbol{Q}(-mathbf{3}, mathbf{2}), boldsymbol{R}(mathbf{5}, mathbf{1}), boldsymbol{S}(mathbf{0},-mathbf{4}) )
What is the ( x- ) coordinate of point ( P )
( ? )
8
49 How many dimension does a surface
has ?
8
50 Plot the points (0,0)(0,3)(3,4)(4,0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle. 8
51 The number of students spent more
than 5 hours in watching ( mathrm{TV}, ) is
A . 32
B.
( c )
D. 14
8
52 Which of the following statements is
false?
A. The x-coordinates of all points to the right of the y-axis are positive
B. The y- coordinates of all points above the x-axis are positive
C. The ( y ) – coordinates of all points below the x-axis are positive
D. The x-coordinates of all points to the left of the y-axis are negative
8
53 If Set B has 200,000 elements,
calculate the difference between
number of negative and even numbers
of set B.

Negative and Even Number Distributions
Numbers
A .25,000
В. 140,000
( c .50,000 )
D. 155,000

8
54 The sales have increase by nearly ( 99.9 % )
from 2007 to 2010 in the case of?
A. Rexona
3. Dettol
( c cdot operatorname{Lux} )
( D . ) Dove
8
55 Fill in the blank:
The system used for describing the position of a is called
Cartesian system.
A. Point
B. Circle
c. Line
D. Square
8
56 For which of these would you use a
histogram to show the data.
The number of letters for different areas
in a postman’s bag.
8
57 Of the following, which best
approximates the percent decrease in
consumption of wood power in the
United States from 2000 to ( 2010 ? )
Renewable Energy Consumption
( A )
B. 11
( c .21 )
( D cdot 26 )
8
58 Reflect shape ( A ) in ( x-a x ) is. Label the
image shape B
8
59 If ( M N ) is a straight line on a cartesian
plane. The co-ordinates of ( mathrm{N} ) are (12,13)
and ( M N=9 ) units. Find the co-
ordinates of ( mathrm{M} )
A ( .(21,13) )
B. (12,22)
c. (12,4)
D. (3,13)
8
60 Position of an object in plane can be easily find out by the help of:
B. Trignometry
c. coordinate geometry
D. Proportions
8
61 A graph drawn using vertical bars is called
A. Bar graph
B. Line graph
c. Pictograph
D. Pie graph
8
62 Find what the following equations become when the origin is shifted to the
point (1,1)( ? )
(i) ( x^{2}+x y-3 x-y+2=0 )
( boldsymbol{x}^{2}-boldsymbol{y}^{2}-boldsymbol{2} boldsymbol{x}+boldsymbol{2} boldsymbol{y}=mathbf{0} )
(iii) ( boldsymbol{x y}-boldsymbol{x}-boldsymbol{y}+mathbf{1}=mathbf{0} )
( boldsymbol{x} boldsymbol{y}-boldsymbol{y}^{2}-boldsymbol{x}+boldsymbol{y}=mathbf{0} )
8
63 What is the percentage of the total sales of laptop in the state of Haryana and Rajasthan for both the years?
Sales of laptop
A . ( 23.13 % )
B . ( 26.54 % )
c. ( 27.4 % )
D. ( 31.34 % )
8
64 The graph shows the number of
basketball titles won by the boys team
and the girls team for three different
school teams.
Based on the data in the graph, which of the following statements is true?
A. The ( F . P . S ) teams together have won the greatest total number of basketball titles
B. The girls L.P.S team has won exactly twice as many titles as the ( G . P . S ) boys and girls teamsm together
C. The girls ( F . P . S ) team has won more titles than the girls ( L . P . S ) team
D. The ( L . P . S ) teams together have won the greatest total number of basketball titles
8
65 The sales of Dove in 2010 was by what
percent less than the sales of Dove in
( 2007 ? )
A. ( 40 % )
3. ( 60 % )
( c .70 % )
( 0.50 % )
8
66 Find the average sales of laptop of all
the states for the year 2004
( A, 9,7 )
3. 11.71
( c .14 .45 )
D. 15.23
8
67 The point X-axis which is equidistant from the point (3,5) and (4,2) is
A. (-6,0)
B . (-7, 0)
c. (7, 0)
D. (-5, 0)
8
68 Figure is a graph of which of the
following?
A ( cdot x^{2}+y^{2}=9 )
в. ( |x|=3 ) and ( |y|=3 )
c. ( |x+y|=3 )
D. ( |x|+|y|=3 )
E . ( x-y=3 )
8
69 In which graph, rectangle bars are separated?
A . line
B. pie
( c . ) bar
D. histogram
8
70 The following histogram shows the
frequency distribution of the ages of 22
teachers in a school:
What is the number of eldest and
youngest teachers in the school?
8
71 Write the name of the point where the
two axes meet.
8
72 What is the ratio of the number of
people who prefer playing Cricket in
2001 to the number of people who prefer
playing Tennis in the year ( 2003 ? )
A . 14: 17
B . 16: 13
c. 15: 11
D. 13: 15
8
73 Which is the highest peak?
( A cdot A )
B. E
( c cdot c )
( D cdot B )
8
74 Which of the points ( A, B, C ) and ( D ) below has the coordinates of the origin?
( A cdot A(-3,1) )
B. B(0, 0)
c. ( c(1,2) )
D. D(9, o)
8
75 Give Reason:
A histogram is a two dimensional
( operatorname{graph} )
8
76 The diagram below shows part of the ( operatorname{graph} ) of ( y=frac{b-x}{c x+d} )
The ( x ) intercept is (6,0)
The vertical asymptote is ( boldsymbol{x}=-3 )
The horizontal asymptote is ( y=-1 )
Find the value of ( boldsymbol{d} )
8
77 Select and write the most appropriate
answer from the given alternatives
for question:
The cartesian equation of the line passing through the points ( boldsymbol{A}(mathbf{4}, mathbf{2}, mathbf{1}) ) and ( boldsymbol{B}(mathbf{2},-mathbf{1}, mathbf{3}) ) is
A. ( frac{x+4}{2}=frac{y-2}{3}=frac{z-1}{-2} )
в. ( frac{x-4}{-2}=frac{y-2}{-3}=frac{z-1}{-2} )
c. ( frac{x-4}{2}=frac{y-2}{3}=frac{z-1}{-2} )
D. ( frac{x-4}{-2}=frac{y-2}{3}=frac{z-1}{-2} )
8
78 Given ( A ) -B-C the co-ordinate of point ( A ) is the smallest.lf ( mathrm{d}(mathrm{A}, mathrm{B})=7.5, mathrm{d}(mathrm{B}, mathrm{C}):=13,8 )
and the coordinate of point ( mathrm{B} ) is ( 8.5, ) then find the coordinates of points ( A ) and ( C )
( A cdot A leftrightarrow 0, C leftrightarrow 63.2 )
B. ( A leftrightarrow 5, C leftrightarrow 40 )
( mathrm{c} cdot mathrm{A} leftrightarrow 1, mathrm{C} leftrightarrow 22.3 )
D. ( A leftrightarrow 3, C leftrightarrow 18 )
8
79 The sales of Lux in 2010 was by what
percent more than the sales of Rexona
in 2007?
A. ( 60 % )
3. ( 50 % )
( c .80 % )
( 0.90 % )
8
80 What percent to the average sales of
branches ( B_{1} B_{2} ) and ( B_{3} ) in 2007 is the
average sales of branches
( B_{1}, B_{2}, ) and ( B_{6} ) in ( 2006 ? )
( A .75 % )
В. ( 77 % )
( c .87 .5 % )
D. ( 70 % )
8
81 What are the different types of graphs? 8
82 Give Reason:
A histogram is not a diagram.
8
83 If the line ( 2 x+5 y=k ) passes through
origin then ( k= )
( mathbf{A} cdot mathbf{0} )
B.
c. -1
D.
8

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